Numerical Methods in Laminar Flame Propagation: A GAMM-Workshop

211 Pages·1982·5.597 MB·German

by  N. Peters (auth.), Norbert Peters, Jürgen Warnatz (eds.)

Norbert Peters
Jiirgen Warnatz (Eds.)
Numerical Methods
in
Laminar Flame Propagation
Notes on Numerical Fluid Mechanics
(Series Editor: Karl Forster, Stuttgart)
Volume 6
Volume 1 Boundary Algorithms for Multidimensionallnviscid
Hyperbolic Flows (Karl Forster, Ed.)
Volume 2 Proceedings of the Third GAMM-Conference on
Numerical Methods in Fluid Mechanics (Ernst
Heinrich Hirschel, Ed.)
Volume 3 Numerical Methods for the Computation of lnviscid
Transonic Flows with Shock Waves (Arthur Rizzi/
Henri Viviand, EdsJ
Volume 4 Shear Flow in Surface-Oriented Coordinates
(Ernst Heinrich Hirschei/Wilhelm Kordulla)
Volume 5 Proceedings of the Fourth GAMM-Conference on
Numerical Methods in Fluid Mechanics
(Henri Viviand, Ed.)
Volume 6 Numerical Methods in Laminar Flame Propagation
(Norbert Peters/ Jurgen Warnatz, Eds.)
Manuscripts should be well over 100 pages. As they will be reproduced toto
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Norbert Peters/Jurgen Warnatz (Eds)
Numerical Methods
•
1n
Laminar Flame Propagation
A GAMM-Workshop
With 66 Figures
Springer Fachmedien Wiesbaden GmbH
CIP-Kurztitelaufnahme der Deutschen Bibliothek
Numerica! methods in laminar flame propagation:
a GAMM workshop/Norbert Peters; Jiirgen Warnatz
(eds.).
(Notes on numerica! fluid mechanics; Voi. 6)
ISBN 978-3-528-08080-8 ISBN 978-3-663-14006-1 (eBook)
DOI 10.1007/978-3-663-14006-1
NE: Peters, Norbert [Hrsg.); Gesellschaft fiir
Angewandte Mathematik und Mechanik; GT
Ali rights reserved
© Springer Fachmedien Wiesbaden 1982
Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig in 1982
No part of this publication may be reproduced, stored in a retrieval system or
transmitted, mechanical, photocopying, recording or otherwise, without prior
permission of the copyright holder.
ISBN 978-3-528-08080-8
Preface
This volume collects the results of a workshop held at Aachen,
West-Germany, Oct. 12 - Oct. 14, 1981. The purpose in bringing
together scientists actively working in the field of numerical
methods in flame propagation was two-fold:
1. To confront them with recent results obtained by large ac
tivation-energy asymptotics and to check these numerically.
2. To compare different numerical codes and different trans
port models for flat flame calculations with complex che
mistry.
Two test problems were formulated by the editors to meet these
objectives. Test problem A was an unsteady propagating flat
flame with one-step chemistry and Lewis number different from
unity while test problem B was the steady, stoichiometric hy
drogen-air flame with prescribed complex chemistry. The parti
cipants were asked to solve one or both test problems and to
present recent work of their own choice at the meeting.
The results of the numerical calculations of test problem A are
challenging just as much for scientists employing numerical me
thods as for those devoted to large activation-energy asympto
tics: Satisfactory agreement between the five different groups
were obtained only for two out of six cases, those with Lewis
number Le equal to one. The very strong oscillations that oc
cur at Le = 2 and a nondimensional activation energy of 20
were accurately resolved only by one group. This case is par
ticular interesting because the asymptotic theory so far pre
dicts instability but not oscillations. This stimulated a nu
merical study by B. Rogg, who determined the boundary between
the stable and oscillating regimes. Although the paper was not
presented at the meeting, it is included in this volume.
On the other hand, test problem B confirmed the expectation
that the existing codes for one-dimensional flat flames with
complex chemistry yield satisfactory results if a non-uniform
v
grid is used with enough (about 25) grid points within the
flame front. With the kinetics prescribed, the fairly large
deviations in calculated flame speeds are due to the different
transport models used. In spite of the computational effort
involved it seems to be neccessary to use rather complex trans
port models. Some of the papers of Part II of this volume deal
with this question.
The workshop was sponsored by the Deutsche Forschungsgemein
schaft, to which the organiser and the participants owe a spe
cial debt. We also note with thanks the contribution of Ms. B.
Tries in the careful preparation of a major part of the type
scripts.
Aachen, April 1982 Norbert Peters
Jilrgen Warnatz
VI
Contents
Preface
Part I Test Problem A and related papers
Discussion of Test Problem A 1
N. Peters
Activation-Energy Asymptotics of the . . . . . . 15
Plane Premixed Flame
G.s.s. Ludford
Theoretical Implications of Nonequal ...... 29
Diffusivities of Heat and Matter on
the Stability of a Plane Premixed
Flame
N. Peters
The Effect of Lewis Number Greater ...... 38
than One on an Unsteady Propagating
Flame with One-step
Ch~mistry
B. Rogg
Part II Test Problem B and related papers
Discussion of Test Problem B ...... 49
J. Warnatz
On the Use of Adaptive Grids in Nume •••••• 65
rically Calculating Adiabatic Flame
Speeds
M.D. Smooke, J.A. Miller, R.J. Kee
Results of a Study of Several Trans . . . . . . 71
port Algorithms for Premixed, Laminar
Steady-State Flames
J.M. Heimerl, T.P. Coffee
VII
Influence of Transport Models and 87
Boundary Conditions on Flame
Structure
J. Warnatz
Numerical Solution of Burner-Stabi .••••. 112
lized Premixed Laminar Flames by an
Efficient Boundary Value Method
M.D. Smooke, J.A. Miller, R.J. Kee
Toward the Formulation of a Global ..•••• 130
Local Equilibrium Kinetics Model
for Laminar Hydrocarbon Flames
R.D. Reitz, F.V. Bracco
Time-Dependent Simulation of Flames ••••.• 152
in Hydrogen-Oxygen-Nitrogen Mixtures
K. Kailasanath, E.S. Oran, J.P. Boris,
T.R. Young
Mechanism of Flame Propagation in •••••• 167
Hydrogen-Air and Methane-Air Systems
S. Fukutani, H. Jinno
Flames near Rich Flammability Limits, •••••. 182
with Particular Reference to the
Hydrogen-Air and Similar Systems
N.R. Carter, M.A. Cherian, G. Dixon-Lewis
Experimental Investigation of Internal •••••• 192
Combustion of Various Fuels
W. MUller
VIII
DISCUSSION OF TEST PROBLEM A
by
N. Peters
Institut fUr Allgemeine Mechanik
Rheinisch-Westf~lische Technische Hochschule Aachen
Aachen, West Germany
ABSTRACT
This is a summary of the results of the five groups that have
calculated the test problem A of the GAMM-Workshop on Numerical
Methods in Laminar Flame Propagation. The test problem is formu
lated and the six different test cases are defined. The numeri
cal methods of solution and the used grid point system are des
cribed and the numerical results are discussed. For the cases
with Le = 1 a good agreement is achieved with all methods. For
Le > 2 oscillations may occur that require a very sensitive
grid adaption in time direction. It is concluded that extreme
care must be taken in calculating unsteady flames with Lewis
numbers different from unity.
1. INTRODUCTION
The test problem A treats the one-dimensional unsteady flame